# Original Sudoku

level: deep

position: .2....78.4.......6.9..7..1....5....3.....1.......9.12..7..1.8..5....4.....67.3... initial

# Autosolve

position: .2....78.4.7.....6.9..7..1....5....3.....1.......9.12..7..1.8..5....4.....67.3... autosolve

# Pair Reduction Variants

## Deep Constraint Pair Analysis

Time used: 0:00:00.000005

List of important HDP chains detected for I8,I9: 1..:

```* DIS # I8: 1 # B6: 3,8 => CTR => B6: 4,5,6
* CNT   1 HDP CHAINS /  26 HYP OPENED
```

List of important HDP chains detected for B2,D2: 1..:

```* DIS # B2: 1 # C8: 3,8 => CTR => C8: 1,2,9
* DIS # B2: 1 + C8: 1,2,9 # B5: 4,8 => CTR => B5: 3,5,6
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 # B6: 4,8 => CTR => B6: 3,5,6
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # E1: 3,6 => CTR => E1: 4,5
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 # B4: 4,8 => CTR => B4: 6
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 + B4: 6 => CTR => B2: 3,5,8
* STA B2: 3,5,8
* CNT   6 HDP CHAINS /  24 HYP OPENED
```

List of important HDP chains detected for D1,D2: 1..:

```* DIS # D1: 1 # C8: 3,8 => CTR => C8: 1,2,9
* DIS # D1: 1 + C8: 1,2,9 # B5: 4,8 => CTR => B5: 3,5,6
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 # B6: 4,8 => CTR => B6: 3,5,6
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # E1: 3,6 => CTR => E1: 4,5
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 # B4: 4,8 => CTR => B4: 6
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 + B4: 6 => CTR => D1: 3,4,6,9
* STA D1: 3,4,6,9
* CNT   6 HDP CHAINS /  24 HYP OPENED
```

List of important HDP chains detected for F4,F6: 7..:

```* DIS # F6: 7 # A5: 3,8 => CTR => A5: 2,7,9
* CNT   1 HDP CHAINS /  27 HYP OPENED
```

See Appendix: Full HDP Chains for full list of HDP chains.

# Details

This sudoku is deep. Here is some information that may be helpful on how to proceed.

## Positions

 .2....78.4.......6.9..7..1....5....3.....1.......9.12..7..1.8..5....4.....67.3... initial .2....78.4.7.....6.9..7..1....5....3.....1.......9.12..7..1.8..5....4.....67.3... autosolve

level: deep

## Pairing Analysis

```--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,D2: 1.. / D1 = 1  =>  4 pairs (_) / D2 = 1  =>  0 pairs (_)
I8,I9: 1.. / I8 = 1  =>  5 pairs (_) / I9 = 1  =>  1 pairs (_)
B2,D2: 1.. / B2 = 1  =>  4 pairs (_) / D2 = 1  =>  0 pairs (_)
C7,B9: 4.. / C7 = 4  =>  1 pairs (_) / B9 = 4  =>  1 pairs (_)
F7,E9: 5.. / F7 = 5  =>  2 pairs (_) / E9 = 5  =>  2 pairs (_)
A1,A3: 6.. / A1 = 6  =>  2 pairs (_) / A3 = 6  =>  1 pairs (_)
F4,F6: 7.. / F4 = 7  =>  1 pairs (_) / F6 = 7  =>  1 pairs (_)
H8,I8: 7.. / H8 = 7  =>  4 pairs (_) / I8 = 7  =>  1 pairs (_)
I5,I6: 8.. / I5 = 8  =>  0 pairs (_) / I6 = 8  =>  2 pairs (_)
* DURATION: 0:00:08.196975  START: 19:23:03.670250  END: 19:23:11.867225 2017-04-29
* CP COUNT: (9)

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
I8,I9: 1.. / I8 = 1 ==>  5 pairs (_) / I9 = 1 ==>  1 pairs (_)
H8,I8: 7.. / H8 = 7 ==>  4 pairs (_) / I8 = 7 ==>  1 pairs (_)
B2,D2: 1.. / B2 = 1 ==>  0 pairs (X) / D2 = 1  =>  0 pairs (_)
D1,D2: 1.. / D1 = 1 ==>  0 pairs (X) / D2 = 1  =>  0 pairs (_)
F7,E9: 5.. / F7 = 5 ==>  2 pairs (_) / E9 = 5 ==>  2 pairs (_)
A1,A3: 6.. / A1 = 6 ==>  2 pairs (_) / A3 = 6 ==>  1 pairs (_)
I5,I6: 8.. / I5 = 8 ==>  0 pairs (_) / I6 = 8 ==>  2 pairs (_)
F4,F6: 7.. / F4 = 7 ==>  1 pairs (_) / F6 = 7 ==>  1 pairs (_)
C7,B9: 4.. / C7 = 4 ==>  1 pairs (_) / B9 = 4 ==>  1 pairs (_)
* DURATION: 0:02:00.658507  START: 19:23:11.867609  END: 19:25:12.526116 2017-04-29
* REASONING I8,I9: 1..
* DIS # I8: 1 # B6: 3,8 => CTR => B6: 4,5,6
* CNT   1 HDP CHAINS /  26 HYP OPENED
* REASONING B2,D2: 1..
* DIS # B2: 1 # C8: 3,8 => CTR => C8: 1,2,9
* DIS # B2: 1 + C8: 1,2,9 # B5: 4,8 => CTR => B5: 3,5,6
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 # B6: 4,8 => CTR => B6: 3,5,6
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # E1: 3,6 => CTR => E1: 4,5
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 # B4: 4,8 => CTR => B4: 6
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 + B4: 6 => CTR => B2: 3,5,8
* STA B2: 3,5,8
* CNT   6 HDP CHAINS /  24 HYP OPENED
* REASONING D1,D2: 1..
* DIS # D1: 1 # C8: 3,8 => CTR => C8: 1,2,9
* DIS # D1: 1 + C8: 1,2,9 # B5: 4,8 => CTR => B5: 3,5,6
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 # B6: 4,8 => CTR => B6: 3,5,6
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # E1: 3,6 => CTR => E1: 4,5
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 # B4: 4,8 => CTR => B4: 6
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 + B4: 6 => CTR => D1: 3,4,6,9
* STA D1: 3,4,6,9
* CNT   6 HDP CHAINS /  24 HYP OPENED
* REASONING F4,F6: 7..
* DIS # F6: 7 # A5: 3,8 => CTR => A5: 2,7,9
* CNT   1 HDP CHAINS /  27 HYP OPENED
* DCP COUNT: (9)
* CLUE FOUND
```

```29;7;elev;22;11.80;1.20;1.20
```

# Appendix: Full HDP Chains

## A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for I8,I9: 1..:

```* INC # I8: 1 # A5: 7,8 => UNS
* INC # I8: 1 # A5: 2,3,9 => UNS
* INC # I8: 1 # A6: 7,8 => UNS
* INC # I8: 1 # F6: 7,8 => UNS
* INC # I8: 1 # C8: 3,8 => UNS
* INC # I8: 1 # C8: 2,9 => UNS
* INC # I8: 1 # B2: 3,8 => UNS
* INC # I8: 1 # B5: 3,8 => UNS
* DIS # I8: 1 # B6: 3,8 => CTR => B6: 4,5,6
* INC # I8: 1 + B6: 4,5,6 # C8: 3,8 => UNS
* INC # I8: 1 + B6: 4,5,6 # C8: 2,9 => UNS
* INC # I8: 1 + B6: 4,5,6 # B2: 3,8 => UNS
* INC # I8: 1 + B6: 4,5,6 # B5: 3,8 => UNS
* INC # I8: 1 + B6: 4,5,6 # A5: 7,8 => UNS
* INC # I8: 1 + B6: 4,5,6 # A5: 2,3,9 => UNS
* INC # I8: 1 + B6: 4,5,6 # A6: 7,8 => UNS
* INC # I8: 1 + B6: 4,5,6 # F6: 7,8 => UNS
* INC # I8: 1 + B6: 4,5,6 # C8: 3,8 => UNS
* INC # I8: 1 + B6: 4,5,6 # C8: 2,9 => UNS
* INC # I8: 1 + B6: 4,5,6 # B2: 3,8 => UNS
* INC # I8: 1 + B6: 4,5,6 # B5: 3,8 => UNS
* INC # I8: 1 + B6: 4,5,6 => UNS
* INC # I9: 1 # B4: 4,8 => UNS
* INC # I9: 1 # B5: 4,8 => UNS
* INC # I9: 1 # B6: 4,8 => UNS
* INC # I9: 1 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED
```

Full list of HDP chains traversed for H8,I8: 7..:

```* INC # H8: 7 # A5: 7,8 => UNS
* INC # H8: 7 # A5: 2,3,9 => UNS
* INC # H8: 7 # A6: 7,8 => UNS
* INC # H8: 7 # F6: 7,8 => UNS
* INC # H8: 7 => UNS
* INC # I8: 7 # B4: 4,8 => UNS
* INC # I8: 7 # B5: 4,8 => UNS
* INC # I8: 7 # B6: 4,8 => UNS
* INC # I8: 7 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED
```

Full list of HDP chains traversed for B2,D2: 1..:

```* INC # B2: 1 # A3: 3,6 => UNS
* INC # B2: 1 # A3: 8 => UNS
* INC # B2: 1 # E1: 3,6 => UNS
* INC # B2: 1 # E1: 4,5 => UNS
* INC # B2: 1 # C3: 3,5 => UNS
* INC # B2: 1 # C3: 8 => UNS
* INC # B2: 1 # E1: 3,5 => UNS
* INC # B2: 1 # E1: 4,6 => UNS
* DIS # B2: 1 # C8: 3,8 => CTR => C8: 1,2,9
* INC # B2: 1 + C8: 1,2,9 # B5: 3,8 => UNS
* INC # B2: 1 + C8: 1,2,9 # B6: 3,8 => UNS
* INC # B2: 1 + C8: 1,2,9 # B4: 4,8 => UNS
* DIS # B2: 1 + C8: 1,2,9 # B5: 4,8 => CTR => B5: 3,5,6
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 # B6: 4,8 => CTR => B6: 3,5,6
* INC # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # B4: 4,8 => UNS
* INC # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # B4: 6 => UNS
* INC # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # B4: 4,8 => UNS
* INC # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # B4: 6 => UNS
* INC # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # A3: 3,6 => UNS
* INC # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # A3: 8 => UNS
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # E1: 3,6 => CTR => E1: 4,5
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 # B4: 4,8 => CTR => B4: 6
* DIS # B2: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 + B4: 6 => CTR => B2: 3,5,8
* INC B2: 3,5,8 # D2: 1 => UNS
* STA B2: 3,5,8
* CNT  24 HDP CHAINS /  24 HYP OPENED
```

Full list of HDP chains traversed for D1,D2: 1..:

```* INC # D1: 1 # A3: 3,6 => UNS
* INC # D1: 1 # A3: 8 => UNS
* INC # D1: 1 # E1: 3,6 => UNS
* INC # D1: 1 # E1: 4,5 => UNS
* INC # D1: 1 # C3: 3,5 => UNS
* INC # D1: 1 # C3: 8 => UNS
* INC # D1: 1 # E1: 3,5 => UNS
* INC # D1: 1 # E1: 4,6 => UNS
* DIS # D1: 1 # C8: 3,8 => CTR => C8: 1,2,9
* INC # D1: 1 + C8: 1,2,9 # B5: 3,8 => UNS
* INC # D1: 1 + C8: 1,2,9 # B6: 3,8 => UNS
* INC # D1: 1 + C8: 1,2,9 # B4: 4,8 => UNS
* DIS # D1: 1 + C8: 1,2,9 # B5: 4,8 => CTR => B5: 3,5,6
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 # B6: 4,8 => CTR => B6: 3,5,6
* INC # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # B4: 4,8 => UNS
* INC # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # B4: 6 => UNS
* INC # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # B4: 4,8 => UNS
* INC # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # B4: 6 => UNS
* INC # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # A3: 3,6 => UNS
* INC # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # A3: 8 => UNS
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 # E1: 3,6 => CTR => E1: 4,5
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 # B4: 4,8 => CTR => B4: 6
* DIS # D1: 1 + C8: 1,2,9 + B5: 3,5,6 + B6: 3,5,6 + E1: 4,5 + B4: 6 => CTR => D1: 3,4,6,9
* INC D1: 3,4,6,9 # D2: 1 => UNS
* STA D1: 3,4,6,9
* CNT  24 HDP CHAINS /  24 HYP OPENED
```

Full list of HDP chains traversed for F7,E9: 5..:

```* INC # F7: 5 # D8: 2,8 => UNS
* INC # F7: 5 # E8: 2,8 => UNS
* INC # F7: 5 # A9: 2,8 => UNS
* INC # F7: 5 # A9: 1,9 => UNS
* INC # F7: 5 # E2: 2,8 => UNS
* INC # F7: 5 # E4: 2,8 => UNS
* INC # F7: 5 # E5: 2,8 => UNS
* INC # F7: 5 => UNS
* INC # E9: 5 # C8: 1,3 => UNS
* INC # E9: 5 # C8: 2,9 => UNS
* INC # E9: 5 # B2: 1,3 => UNS
* INC # E9: 5 # B2: 5,8 => UNS
* INC # E9: 5 # H7: 4,9 => UNS
* INC # E9: 5 # I7: 4,9 => UNS
* INC # E9: 5 # G9: 4,9 => UNS
* INC # E9: 5 # I9: 4,9 => UNS
* INC # E9: 5 # H4: 4,9 => UNS
* INC # E9: 5 # H5: 4,9 => UNS
* INC # E9: 5 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED
```

Full list of HDP chains traversed for A1,A3: 6..:

```* INC # A1: 6 # B2: 3,8 => UNS
* INC # A1: 6 # C3: 3,8 => UNS
* INC # A1: 6 # D3: 3,8 => UNS
* INC # A1: 6 # D3: 2,4,6 => UNS
* INC # A1: 6 # A5: 3,8 => UNS
* INC # A1: 6 # A6: 3,8 => UNS
* INC # A1: 6 # F2: 5,9 => UNS
* INC # A1: 6 # F2: 2,8 => UNS
* INC # A1: 6 # I1: 5,9 => UNS
* INC # A1: 6 # I1: 4 => UNS
* INC # A1: 6 # F7: 5,9 => UNS
* INC # A1: 6 # F7: 2,6 => UNS
* INC # A1: 6 => UNS
* INC # A3: 6 # C1: 1,3 => UNS
* INC # A3: 6 # B2: 1,3 => UNS
* INC # A3: 6 # D1: 1,3 => UNS
* INC # A3: 6 # D1: 4,6,9 => UNS
* INC # A3: 6 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED
```

Full list of HDP chains traversed for I5,I6: 8..:

```* INC # I6: 8 # A5: 3,7 => UNS
* INC # I6: 8 # A5: 2,8,9 => UNS
* INC # I6: 8 # F4: 6,7 => UNS
* INC # I6: 8 # F4: 2,8 => UNS
* INC # I6: 8 => UNS
* INC # I5: 8 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED
```

Full list of HDP chains traversed for F4,F6: 7..:

```* INC # F4: 7 # E4: 6,8 => UNS
* INC # F4: 7 # D5: 6,8 => UNS
* INC # F4: 7 # E5: 6,8 => UNS
* INC # F4: 7 # D6: 6,8 => UNS
* INC # F4: 7 # B6: 6,8 => UNS
* INC # F4: 7 # B6: 3,4,5 => UNS
* INC # F4: 7 # F3: 6,8 => UNS
* INC # F4: 7 # F3: 2,5 => UNS
* INC # F4: 7 => UNS
* DIS # F6: 7 # A5: 3,8 => CTR => A5: 2,7,9
* INC # F6: 7 + A5: 2,7,9 # B5: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # C5: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # B6: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # C6: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # D6: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # D6: 4,6 => UNS
* INC # F6: 7 + A5: 2,7,9 # A3: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # A3: 6 => UNS
* INC # F6: 7 + A5: 2,7,9 # B5: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # C5: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # B6: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # C6: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # D6: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # D6: 4,6 => UNS
* INC # F6: 7 + A5: 2,7,9 # A3: 3,8 => UNS
* INC # F6: 7 + A5: 2,7,9 # A3: 6 => UNS
* INC # F6: 7 + A5: 2,7,9 => UNS
* CNT  27 HDP CHAINS /  27 HYP OPENED
```

Full list of HDP chains traversed for C7,B9: 4..:

```* INC # C7: 4 # B8: 1,8 => UNS
* INC # C7: 4 # C8: 1,8 => UNS
* INC # C7: 4 # A9: 1,8 => UNS
* INC # C7: 4 # B2: 1,8 => UNS
* INC # C7: 4 # B4: 1,8 => UNS
* INC # C7: 4 => UNS
* INC # B9: 4 # H7: 5,9 => UNS
* INC # B9: 4 # I7: 5,9 => UNS
* INC # B9: 4 # G9: 5,9 => UNS
* INC # B9: 4 # I9: 5,9 => UNS
* INC # B9: 4 # H2: 5,9 => UNS
* INC # B9: 4 # H5: 5,9 => UNS
* INC # B9: 4 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED
```